Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs

In this paper, we prove a convergence theorem for singular perturbations problems class of fully nonlinear parabolic partial differential equations (PDEs) with ergodic structures. The limit function is represented as the viscosity solution to degenerate PDEs. Our approach mainly based on G-stochastic analysis argument. As byproduct, also establish averaging principle stochastic driven by G-Brownian motion (G-SDEs) two time-scales. results extend Khasminskii’s case.